1. The centre of a given circle can be located by drawing
Answer: D. the perpendicular bisectors of two non-parallel chords
Mathematics Class 10 Unit 11: Practical Geometry of Circles MCQs
33 multiple choice questions with the correct answer for each. Tap an option to check yourself, or switch on "Show all answers".
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2. The perpendicular bisector of any chord of a circle passes through
Answer: A. the centre of the circle
3. To draw a circle through three non-collinear points A, B and C, the centre is found at the intersection of
Answer: B. the perpendicular bisectors of AB and BC
4. A circle passing through all three vertices of a triangle is called its
Answer: C. circumcircle
5. To complete a circle when only a part of its arc is given, we first choose
Answer: C. three points on the arc
6. The tangent at a point P of a circle with centre O is drawn
Answer: B. perpendicular to OP at P
7. If PT is a tangent at P to a circle with centre O, then angle OPT measures
Answer: A. 90°
8. To draw a tangent to a circle from an external point P, we draw a circle on OP as diameter where O is the centre. This circle cuts the given circle at
Answer: D. the points of contact of the tangents
9. In drawing tangents from an external point P, angle OTP is 90° because it is
Answer: A. an angle in a semicircle
10. The number of tangents drawn from an external point to a circle is
Answer: B. 2
11. A tangent drawn at a point on a circle is
Answer: C. unique
12. The centre of a circle which touches a given line at a given point lies on
Answer: D. the perpendicular to the line at that point
13. Two tangents to a circle meet at an angle of 60°. The angle between the radii drawn to the points of contact is
Answer: B. 120°
14. Two tangents to a circle meet at an angle of 90°. The angle between the radii drawn to the points of contact is
Answer: D. 90°
15. To draw two tangents to a circle meeting at an angle of 70°, the angle between the radii to the points of contact is
Answer: A. 110°
16. A common tangent that does not cross the line segment joining the centres of two circles is called a
Answer: C. direct (external) common tangent
17. A common tangent that crosses the line segment joining the centres of two circles is called a
Answer: A. transverse (internal) common tangent
18. The maximum number of common tangents of two circles is
Answer: B. 4
19. The number of common tangents of two separate circles (neither touching nor intersecting, each outside the other) is
Answer: C. 4
20. The number of common tangents of two circles touching externally is
Answer: D. 3
21. The number of common tangents of two circles touching internally is
Answer: B. 1
22. The number of common tangents of two circles intersecting at two points is
Answer: A. 2
23. The number of common tangents of two circles, one lying completely inside the other without touching, is
Answer: C. 0
24. For two circles touching externally, the transverse common tangent passes through
Answer: D. the point of contact
25. Direct common tangents to two equal circles are
Answer: B. parallel to each other
26. The length of a direct common tangent to two circles with radii r₁, r₂ and distance d between centres is
Answer: D. √(d² − (r₁ − r₂)²)
27. The length of a transverse common tangent to two circles with radii r₁, r₂ and distance d between centres is
Answer: A. √(d² − (r₁ + r₂)²)
28. Two circles of radii 8 cm and 3 cm have their centres 13 cm apart. The length of a direct common tangent is
Answer: C. 12 cm
29. Two circles of radii 7 cm and 5 cm have their centres 13 cm apart. The length of a transverse common tangent is
Answer: A. 5 cm
30. A tangent PT is drawn from a point P that is 10 cm from the centre of a circle of radius 6 cm. The length PT is
Answer: B. 8 cm
31. The midpoint of the segment OP is found in the construction of tangents from P by drawing
Answer: C. the perpendicular bisector of OP
32. Instruments normally used for geometrical constructions of circles are
Answer: D. compass and straightedge (ruler)
33. To find the radius of a circle from part of its arc, after finding the centre we measure
Answer: C. the distance from the centre to any point on the arc
About Mathematics Class 10 Unit 11 MCQs (Federal Board)
These 33 Mathematics MCQs cover Class 10 Unit 11: Practical Geometry of Circles of the Federal Board (FBISE) SSC-II (Class 10) syllabus. They are SLO-based MCQs as per the new pattern for FBISE exams. Each question has four options and the correct answer is shown, so you can practise for the annual examination and find the topics you still need to revise. Download the Practical Geometry of Circles MCQs as a PDF using the button at the top of this page.